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DTIC AD0631865: SOME CODES WHICH ARE INVARIENT UNDER A DOUBLY-TRANSITIVE PERMUTATION GROUP AND THEIR CONNECTION WITH BALANCED INCOMPLETE BLOCK DESIGNS

by: Defense Technical Information Center

Publication date: 1966-01-28

Topics: DTIC Archive, , HAWAII UNIV HONOLULU (MANOA CAMPUS) DEPT OF ELECTRICAL ENGINEERING, *COMBINATORIAL ANALYSIS, CODING, GROUPS(MATHEMATICS), INVARIANCE, PERMUTATIONS,

Collection: dticarchive; additional_collections

Language: English

If a binary code is invariant under a doubly-transitive permutation group, then the set of all code words of weight j forms a balanced incomplete block design. Besides the extended normal BCH codes and the extended quadratic residue codes, the Reed-Muller codes are proven to be invariant under a doubly- transitive permutation group. Thus, BIB designs can be derived from these classes of codes. It is shown that if the symbols of the Reed-Muller codes are properly arranged, and if the first digit is omitted, then all Reed-Muller codes are cyclic.